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  4. Estimation in short-panel data models with bilinear errors

Estimation in short-panel data models with bilinear errors

MMC.
2023;
Volume 10, Number 3
: pp. 682–692
https://doi.org/10.23939/mmc2023.03.682
Received: February 16, 2023
Revised: July 12, 2023
Accepted: July 13, 2023

Mathematical Modeling and Computing, Vol. 10, No. 3, pp. 682–692 (2023)

Authors:
  1. A. Lmakri
  2. A. Akharif
  3. A. Mellouk
1
National Higher School of Arts and Crafts (ENSAM), Hassan II University, Casablanca, Morocco
2
Mathematics and Applications Laboratory, FSTT, Abdelmalek Essaadi University Tetouan, Morocco
3
Regional Center for Education and Training Trades, Tangier, Morocco

Many estimation methods have been proposed for the parameters of the regression models with serially correlated errors.  In this work, we develop an asymptotic theory for estimation in the short panel data models with bilinear error.  We propose a comparative study by simulation between several estimators (adaptive, ordinary and weighted least squares) for the coefficients of panel data models when the errors are bilinear serially correlated.  As a consequence of the uniform local asymptotic normality property, we obtain adaptive estimates of the parameters.  Finally, we illustrate the performance of the proposed estimators via  Monte Carlo simulation study.  We show that the adaptive estimates are more efficient than the weighted and ordinary least squares estimates.

adaptive estimate
bilinear models
panel regression models
weighted least squares
ordinary least squares
  1. Lillard L. A., Willis R. J.  Dynamic aspects of learning mobility.  Econometrica.  46 (5), 985–1012 (1978).
  2. Bhargava A., Franzini L., Narendranathan W.  Serial correlation and the fixed effects model.  The Review of Economic Studies.  49 (4), 533–549 (1982).
  3. Nicholls D. F., Pagan A. R., Terrell R. D.  The estimation and use of models with moving average disturbance terms: A survey.  International Economic Review.  16 (1), 113–134 (1975).
  4. Abonazel M. R.  Different estimators for stochastic parameter panel data models with serially correlated errors.  Journal of Statistics Applications & Probability.  7 (3), 423–434 (2018).
  5. Baltagi B., Li Q.  Testing AR(1) against MA(1) disturbances in an error component model.  Journal of Econometrics.  68 (1), 133–151 (1995).
  6. Allal J., El Melhaoui S.  Tests de rangs adaptatifs pour les modèles de régression linéaire avec erreurs ARMA.  Annales des Sciences Mathématiques du Québec.  30, 29–54 (2006).
  7. Dutta H.  Large sample tests for a regression model with autoregressive conditional heteroscedastic errors.  Communications in Statistics – Theory and Methods.  28 (1), 105–117 (1999).
  8. Elmezouar Z. C., Kadi A. M., Gabr M. M.  Linear regression with bilinear time series errors.  PanAmerican Mathematical Journal.  22 (1), 1–13 (2012).
  9. Hallin M., Taniguchi M., Serroukh A., Choy K.  Local asymptotic normality for regression models with long-memory disturbance.  The Annals of Statistics.  27 (6), 2054–2080 (1999).
  10. Hwang S. Y., Basawa I. V.  Asymptotic optimal inference for a class of nonlinear time series models.  Stochastic Processes and their Applications.  46 (1), 91–113 (1993).
  11. Ling S., Peng L., Zhu F.  Inference for a special bilinear time series model.  Journal of Time Series Analysis.  36 (1), 61–66 (2015).
  12. Jiang J.  Linear and Generalized Linear Mixed Models and Their Applications.  Springer, New York (2007).
  13. Lmakri A., Akharif A., Mellouk A.  Optimal detection of bilinear dependence in short panels of regression data.  Revista Colombiana de Estadística.  43 (2), 143–171 (2020).
  14. Drost F. C., Klaassen C. A. J.  Efficient estimation in semiparametric GARCH models.  Journal of Econometrics.  81 (1), 193–221 (1997).
  15. Ling S., McAleer M.  Adaptive estimation in nonstationry ARMA models with GARCH noises.  The Annals of Statistics.  31 (2), 642–674 (2003).
  16. Le Cam L., Yang G. L.  Asymptotics in Statistics.  Springer, US (1990).
  17. Hájek J. A.  Characterization of limiting distributions of regular estimates.  Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete.  14, 323–330 (1970).
  18. Rao C. R.  Linear Statistical Inference and Its Applications.  Wiley, New York (1965).
  19. Schick A.  On efficient estimation in regression models.  The Annals of Statistics.  21 (3), 1486–1521 (1993).
  20. Koul H. L., Schick A.  Efficient estimation in nonlinear autoregressive time series models.  Bernoulli.  3, 247–277 (1997).